The present invention relates to adaptive fractionally-spaced equalizers which mitigate the distorting effects of linearly dispersive channels on bandlimited spectrally shaped data signals. More particularly, the invention relates to apparatus which permits Nyquist-rate updating and control of the equalizer coefficients, thereby eliminating the phenomenon of coefficient drift and also permitting more rapid coefficient adaptation.
Fractionally spaced equalizers are invaluable for the reliable and accurate reception of spectrally-shaped bandlimited data signals transmitted over unknown, linearly-dispersive channels. The equalizers are commonly implemented as adaptive transverse filters in which successive delayed versions of the incoming signal are weighted by a vector of tap coefficients. The weighted products are subsequently added together to form the output signal, which, when appropriately quantized ("sliced"), permits recovery of the transmitted data symbols. These transmitted data symbols, appearing once per baud interval, T, are either: known a priori at the receiver, as in the case of start-up episodes requiring training sequences; or are unknown at the receiver, as in the case of decision-directed equalizer adaptation. In this latter mode, the equalizer provides estimates of the transmitted symbol states.
For either arrangement, the known or estimated symbol state is subtracted from the actual equalizer output once per symbol period, thus generating a baud-rate error signal that is used to update all tap coefficients in such a way as to minimize a measure of distortion associated with the incoming corrupted signal. Common measures of distortion include peak distortion and mean-squared-error distortion. Equalizers employ to minimize peak distortion use a zero-forcing control algorithm to adjust tap coefficients so as to minimize the average of the absolute value of the aforementioned error signal. Equalizers minimizing mean-squared error use a tap adjustment algorithm which minimizes the average value of the square of the same error signal.
In the prior art, most applications of adaptive equalizers have utilized synchronous, or baud-rate, equalizers. In that arrangement, the tapped delay line of the transversal filter is made up of a series of symbol-period-spaced delay elements of T-seconds each. The distorted received signal is successively delayed at the baud-rate, which each delayed version passing on to tap coefficients for appropriate signal weighting. More recently, however, the importance of fractionally spaced equalizers has been recognized. Fractionally spaced equalizers are made up of tapped delay-line elements, each of which is less than a symbol period. Because of these shorter delay sections, the fractionally spaced equalizer is able to adaptively form an optimal matched receiver (a matched filter followed by a synchronous transversal equalizer) and exhibits an insensitivity to channel delay distortion, including timing phase errors (See R. D. Gitlin and S. B. Weinstein, "Fractionally Spaced Equalization: An Improved Digital Transversal Equalizer," B.S.T.J., Vol. 60, No. 2, February 1981, pp. 275-296). Fractionally spaced equalizers, like synchronous equalizers, achieve tap coefficient control by generating an error signal once per symbol period by comparing the equalized output against a known or estimated symbol state.
Fractionally spaced equalizers suffer from one unique but notable problem. Unlike their synchronous counterparts with one set of clearly optimum tap coefficients providing the least mean-squared error, fractionally-spaced equalizers have many coefficient sets that afford approximately the same mean-squared error. Consequently, any bias or perturbation in coefficient updating can cause some of the coefficients to drift to very large values though the average mean-square error at the output is at or near a minimum value. When these drifting coefficients reach bounds set by implementation, the equalizer can experience partial or total failure with severe implications for transmission system integrity.
Approaches in the prior art for remedying this problem are described by G. Ungerboeck ("Fractional Tap-Spacing Equalizers and Consequences for Clock Recovery for Data Modems," IEEE Trans. on Communications. Vol. COM-24, No. 8, August 1976, pp. 856-864); R. D. Gitlin, H. C. Meadors, Jr., and S. B. Weinstein ("The Tap-Leakage Algorithm: An Algorithm for the Stable Operation of a Digitally Implemented, Fractionally Spaced Adaptive Equalizer," B.S.T.J. Vol. 61, No. 8, October 1982, pp. 1817-1839 and in U.S. Pat. No. 4,237,554, entitled Coefficient Tap Leakage for Fractionally-Spaced Equalizers issued on Dec. 2, 1980); and in U.S. Pat. No. 4,376,308, entitled Control of Coefficient Drift for Fractionally Spaced Equalizers issued on Mar. 8, 1983 to B. E. McNair.
Ungerboeck, noting that the fractionally spaced equalizer instability is associated with coefficient drift to larger and larger values, recommended the introduction of a leakage term into the coefficient updating algorithm. More specifically, the recommended leakage term was intimately related to the magnitude of the equalizer coefficient, thus attacking the symptom rather than the cause. The approach of Messrs. Gitlin, Meadors and Weinstein also relies on tap leakage, but in their technique the leakage factor is independent of the coefficient and specifically treats a major cause of coefficient drift-bias in the digital arithmetic operations of coefficient updating in digitally-implemented equalizers. Finally, the remedy of McNair concerns injecting signal-dependent passband noise into the "no-energy bands" of the otherwise bandlimited signal. The last approach proves efficacious since it has been noted that in the presence of passband noise of sufficiency energy, the fractionally spaced equalizer tends to adaptively form unique coefficient sets, thus ameliorating coefficient drift and obviating the need for tap leakage apparatus.
U.S. Pat. No. 4,384,355 issued to J. J. Werner on May 17, 1983, teaches that the previously described coefficient drift can be controlled by causing the sampled signal to have energy in frequency bands in which the sampled channel transfer function has substantially zero gain, those frequency bands being referred to as "no-energy bands". This is illustratively achieved by adding to the analog data signal an out-of-band analog signal having energy in at least one no-energy band to form a composite signal which is then sampled.
The arrangements of Ungerboeck and Gitlin, Meadors, and Weinstein share a common feature in that they repeatedly leak-off some of the coefficient value. This prevents the unrestricted growth in equalizer coefficients that leads to register overflows and subsequent performance deterioration. For well-conditioned channels, that is, those whose temporal variation and dispersive character are thoroughly understood, this approach is quite satisfactory since the empirical selection of a leakage factor can be made with some foresight. However, for another very broad class of linearly dispersive channels, such as exhibited by terrestrial radio transmission during tropospheric multipath propagation, there exists such a paucity of information about temporal dynamics as to make the appropriate selection of the leakage parameter highly empirical. Also, the leakage approach lends itself to, and has been presented in the context of, digitally-implemented equalizers which minimize the average of the mean-squared error (the related adaptation procedure is referred to as the "linear least-mean-square," or linear LMS, algorithm). Nevertheless, there exist many high-speed applications (&gt;10 MHz) for analog realizations of fractionally spaced equalizers using zero-forcing or established variants of the LMS algorithm. The arrangement of McNair, wherein signal-dependent passband noise is added to the incoming corrupted signal, requires much additional hardware and may potentially degrade a reliable data-symbol-recovery process, particularly if the dispersive channel exhibits an already poor signal-to-noise ratio.
The work of Lucky, Salz and Weldon (Principles of Data Communication, McGraw-Hill Book Company, New York, 1968, Chapter 4) teaches that in most modern bandlimited communication systems, the end-to-end baseband spectrum has a Nyquist shape, thus assuring the absence of intersymbol interference. Furthermore, for purposes of thermal noise immunity with constrained input power, half of this shape is provided at the transmitter by square-root-of-Nyquist filtering, with matched spectral shaping at the receiver. The bandwidth of the resulting digital signal is limited to 1/T', with T'.gtoreq.T, where T is again the symbol period, or signaling interval, of the data communication system. The familiar Nyquist sampling criterion requires that a complete and unique description of a bandlimited signal necessitates time samples at a rate at least twice the highest spectral frequency (this is called the Nyquist rate). We therefore see that adaptive digital filtering at the receiver requires a fractionally spaced equalizer with delayed versions of the input signal at least every T'/2 seconds. In practice, the conventional technique is to satisfy this Nyquist requirement by constructing equalizers with T/2 delay elements in the tapped delay line, since T.ltoreq.T'. In spite of the aforementioned criterion, coefficient adaptation is invariably controlled by generating an error signal once in each symbol period and using this synchronous error signal for appropriate cross correlation and coefficient updating once in each symbol period. It is no surprise, then, that fractionally spaced equalizers experience coefficient drift. Coefficient control achieved via symbol-period-spaced information (in particular, comparing the output signal against an actual or estimated symbol state) equates to a zero-intersymbol-interference channel. Such a channel is Nyquist, by definition and has a minimum value of mean-squared output error, but does not uniquely specify which of an infinite number of Nyquist shapes is achieved. The equalizer coefficients are therefore unrestrained and drift.